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You actually also say la boda, because actually nobody cares about the religious ceremony (unless you are over 60 years old), but about the party thereafter; that's for me the most common word. I'd use only that, unless I want to sound too elegant.
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c.p.Aug 14 '14 at 21:01

If they are Mexicans is probably that the mass will be in a catholic church, that's a "misa" [mass], and then the party will be just the party because "boda"[the wedding] envolves both mass and party but it's normal to call it "la boda" since a lot of people just go to the party "la boda" is accurate for the party, if the day after they make another party in the morning will be "lavado de olla" [Whashing pot] or "recalentado" [reheaded] depending on what part of Mexico they are. "Recepción" and "Banquete" are American concepts but since they live in the US I assume that it will be understood.